Statistical Inference of Reliability with Multivariate Accelerated Degradation Data

doi:10.1007/s12204-019-2124-0

Abstract

Abstract: Accelerated degradation test (ADT) has become an efficient approach to assess the reliability of degradation products within limited time and budget. Some products have more than one degradation process that is responsible for failure of product, which introduces some problems of modeling accelerated degradation data and estimating unknown parameters. In order to solve the problems, a practical method of inferring reliability with multivariate accelerated degradation data is proposed in this paper. Stochastic processes are used to fit accelerated degradation data, and then margin reliability functions are derived from the degradation models. Unlike the traditional assumption that the degradation increments of multivariate degradation processes at the same observing time are mutually dependent, the margin reliabilities at the same time are considered to be dependent, which is applicable to the situation that multivariate degradation data is not simultaneously observed. Copula functions are used to describe the dependency between marginal reliabilities, and the two situations that copula parameter is independent of accelerated stress or dependent on accelerated stress are both considered. In the case study, the bivariate accelerated degradation data of O-ring rubber is used to demonstrate our proposed method. The research results indicate that the proposed method provides a practical and feasible approach to reliability inference with multivariate accelerated degradation data.

Key words: multivariate accelerated degradation| stochastic processes| copula function| marginal reliability

摘要： Accelerated degradation test (ADT) has become an efficient approach to assess the reliability of degradation products within limited time and budget. Some products have more than one degradation process that is responsible for failure of product, which introduces some problems of modeling accelerated degradation data and estimating unknown parameters. In order to solve the problems, a practical method of inferring reliability with multivariate accelerated degradation data is proposed in this paper. Stochastic processes are used to fit accelerated degradation data, and then margin reliability functions are derived from the degradation models. Unlike the traditional assumption that the degradation increments of multivariate degradation processes at the same observing time are mutually dependent, the margin reliabilities at the same time are considered to be dependent, which is applicable to the situation that multivariate degradation data is not simultaneously observed. Copula functions are used to describe the dependency between marginal reliabilities, and the two situations that copula parameter is independent of accelerated stress or dependent on accelerated stress are both considered. In the case study, the bivariate accelerated degradation data of O-ring rubber is used to demonstrate our proposed method. The research results indicate that the proposed method provides a practical and feasible approach to reliability inference with multivariate accelerated degradation data.

关键词: multivariate accelerated degradation| stochastic processes| copula function| marginal reliability

CLC Number:

TB 114.3

ZHOU Yuan (周源), WANG Haowei (王浩伟), Lü Weimin (吕卫民). Statistical Inference of Reliability with Multivariate Accelerated Degradation Data[J]. Journal of Shanghai Jiao Tong University (Science), 2020, 25(2): 237-245.

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